Distance travelled by a vehicle is measured by the odometer — option 4.

The name gives it away. “Odometer” comes from the Greek hodos, meaning path or road, and metron, a measure — literally a measurer of the road covered. It counts the revolutions of the wheel or of the transmission output shaft and multiplies by the wheel’s circumference, so the reading accumulates and never resets. A trip meter is the same mechanism with a reset knob, used to measure a single journey.

Speedometer against odometer — the trap in this question. Both are driven from the same rotating shaft, and both sit on the same dashboard, which is why they are so often confused. The distinction is that the speedometer measures the rate at which distance is being covered at this instant, while the odometer accumulates the total distance. In the language of calculus, the odometer reading is the time integral of the speedometer reading.

The other two are not vehicle instruments at all. An ammeter is connected in series in an electrical circuit to read current, and a chronometer is a precision timekeeper — historically the marine chronometer of John Harrison, which made the determination of longitude at sea possible.

A related instrument is the taximeter, which combines distance from an odometer with waiting time to compute a fare.

Hence, the answer is Odometer.